Previous results [1]}, [2]} on training deep neural networks in practical tasks showed that, for each deep learning optimizer, the number of steps for training the network halves for each doubling of the batch size and diminishing returns exist beyond a critical batch size. Theorem REF  indicates that the number of steps needed for (REF ) decreases as the batch size increases, as is also seen in training deep neural networks [1]}, [2]}. Theorem REF  indicates that critical batch sizes exist in the sense of minimizing the SFO complexities \(N_G(b) b\)  and \(N_D(b) b\) . We are interested in verifying whether or not a critical batch size exists for training GANs. Hence, the next section numerically examines the relationship between the batch size \(b\)  and not only the number of steps \(N\)  but also the SFO complexity \(N b\)  and verifies whether a critical batch \(b^\star \)  exists such that the SFO complexity \(N(b) b\)  is minimized at \(b^\star \) .
